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Spectral form factor near the Ehrenfest time.
Piet W Brouwer1, Saar Rahav, Chushun Tian
1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
Summary
We calculated quantum corrections to spectral form factors in chaotic cavities. Our periodic orbit theory results differ from prior field-theoretic methods for broken time-reversal symmetry, suggesting a potential flaw in existing calculations.
Area of Science:
- Quantum chaos
- Statistical spectroscopy
- Condensed matter physics
Background:
- The spectral form factor (SFF) characterizes quantum chaotic systems.
- Quantum corrections to the SFF reveal details about underlying classical dynamics.
- Periodic orbit theory and field-theoretic methods are key tools for analyzing these corrections.
Purpose of the Study:
- To calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor.
- To compare results from periodic orbit theory with existing field-theoretic calculations.
- To investigate discrepancies in the treatment of classical trajectory encounters.
Main Methods:
- Utilizing periodic orbit theory to analyze quantum corrections.
- Focusing on systems with broken time-reversal symmetry.
- Examining the role of small-angle encounters in classical trajectories.
Main Results:
- The calculated quantum correction to the SFF differs from previous field-theoretic results for two small-angle encounters.
- A potential technical flaw is identified in the existing field-theoretic calculation.
- The agreement between field-theoretic and periodic orbit approaches for multiple encounters remains an open question.
Conclusions:
- Periodic orbit theory provides an alternative framework for calculating quantum corrections to the SFF.
- Discrepancies highlight the need for careful validation of theoretical methods in quantum chaos.
- Further investigation is required to reconcile different theoretical approaches for complex classical dynamics.
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